Question

You wish to estimate, with 95% confidence, the population proportion of tablet owners who use their tablets daily. Your estimate must be accurate within 2% of the population proportion. No preliminary estimate is available. Find the minimum sample size needed.

Answer 1

Solution:
Given in the question
Confidence level = 0.95
alpha() or level of significance = 1 - confidence level = 1 - 0.95 = 0.05
/2 = 0.05/2 = 0.025
Margin of error (E) = 0.02
No preliminary estimate is available for population proportion so p= 0.5
Minimum sample size needed can be calculated as
Minimum sample size n = (Z/2 /E)^2 * (p*(1-p)
At /2 = 0.025 from Z table we found Z/2 = 1.96
So Minimum sample size n = (1.96/0.02)^2 * (0.5*(1-0.5)) = (98)^2 * 0.25 = 2401
So minimum sample size needed = 2401